-4x+y=-5 8x-2y=10 solve by elimination

Question

This is how I worked it:

2(-4x+y=-5) = -8x+2y=-10

8x-2y=10

-8x+2y=-10

(the x and y cancels each other out, leaving 10 and -10, which are false, so I got no solution)

But when I used a calculator, it says it has infinitely many solutions, I'm confused on how but I can only solve this using elimination and not substitution.

Please help, thank you!

Answer 1

You're adding the two equations. On the left side of the equation, the x and y terms cancel out like you said, so you get 0 on the left hand side. On the right side, the 10 and -10 also cancel, so you get 0 on the right side. So, you get 0 = 0, which is always true, so there are infinitely many solutions.